Questions: Examine the following graph of y=-3x+7. Match each x-coordinate with the corresponding y-coordinate.

Examine the following graph of y=-3x+7. Match each x-coordinate with the corresponding y-coordinate.
Transcript text: Examine the following graph of $y=-3 x+7$. Match each $x$-coordinate with the corresponding $y$-coordinate.
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Solution

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Solution Steps

Step 1: Identify the Equation of the Line

The given equation of the line is \( y = -3x + 7 \).

Step 2: Understand the Slope and Y-Intercept

The slope (m) is -3, and the y-intercept (b) is 7. This means the line crosses the y-axis at (0, 7).

Step 3: Calculate Corresponding Y-Coordinates for Given X-Coordinates

To find the y-coordinates for specific x-coordinates, substitute the x-values into the equation \( y = -3x + 7 \).

  1. For \( x = -2 \): \[ y = -3(-2) + 7 = 6 + 7 = 13 \] So, the point is (-2, 13).

  2. For \( x = 0 \): \[ y = -3(0) + 7 = 0 + 7 = 7 \] So, the point is (0, 7).

  3. For \( x = 2 \): \[ y = -3(2) + 7 = -6 + 7 = 1 \] So, the point is (2, 1).

Final Answer

  • For \( x = -2 \), the corresponding \( y \)-coordinate is 13.
  • For \( x = 0 \), the corresponding \( y \)-coordinate is 7.
  • For \( x = 2 \), the corresponding \( y \)-coordinate is 1.
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